The power supply will work without the relay. Missing the relay strongly suggests somebody abused it over and over again, so there may be other faults.
Relay was sourced from P&B, which has been through many changes since 1954, and the part-number is clearly an H-P spec number, not any stock P&B relay. It was very likely hand-adjusted to a specific trip point.
Working how it works: In short, an ~18V ~2K N.O. relay which will stand occasional 500V closure at very low voltage. Since that is a very odd part today, we favor a low-cost part so if it fails after some time we do not cry about replacement.
FTR-F3AA018E-HA Fujitsu, $1.38 at Mouser, 500 in stock
http://bama.edebris.com/download/hp/711a/711a.pdf
https://www.mouser.com/datasheet/2/164/ftr-f3ha-318.pdf
https://www.mouser.com/Electromechanical/Relays/_/N-5g31/